Prepare the OS
Arch Linux ARM - you can get the image file from the Raspberry Pi download page.
Write the image to the SD card. (I use Win32DiskImager)
Expand the main partition to fill the SD card. From my Windows laptop I booted to a GParted Live CD to do this.

Go headless
Change the root password!

passwd root

Set up a fixed IP address. (You may need to change your router settings to define a fixed IP address range) Edit /etc/rc.conf using nano:

You should now have two streams available from your Raspberry Pi. One is an asf stream which you can connect to from players like Windows Media Player or VLC. The other is an mjpeg stream which you can view from a web browser without requiring any plugins.
The mjpeg URL is:

http://192.168.0.101:8090/webcam.mjpeg

The asf stream is:

http://192.168.0.101:8090/webcam.asf

Put it on the Internet
If you just want to see this on the Internet temporarily simply open up port 8090 on your home router firewall settings. Set up an Inbound Service on port 8090 to 192.168.0.101. Now find your external ip address and you should be able to connect through that. Your external address will probably be shown somewhere in your router web interface or you can find it by going to here: http://ip.dnsexit.com/
Your external address will change occasionally unless you have a fixed IP address. In another post I'll show how to set up Dynamic DNS with an address updater so you can reach your Pi on the net through a name rather than address. The updater ensures that if your external address changes the Dynamic DNS provider is given the new one.